Did Neil Armstrong mislead the world about his 'one small step' line?

The famed quote wasn't quite so spontaneous after all, at least according to the late astronaut's brother

One of the first steps taken on the moon by Neil Armstrong and Buzz Aldrin in 1969.

It's one of the
most famous lines in human history: "That's one small step for [a] man,
one giant leap for mankind." Whether Neil Armstrong — who died in August
at age 82 — actually included the "a" has been the subject of debate for decades (he claims it was lost in transmission). And now, thanks to a new BBC documentary, Neil Armstrong — First Man on the Moon, we might finally have our answer.

Brother Dean Armstrong says in the doc that the line
wasn't thought up on the spot like the Apollo 11 mission commander long
suggested. Instead, the astronaut allegedly wrote the phrase down weeks
before the mission, slipping it to his brother on a piece of paper as
they played a game of Risk. "Before he went to Cape, he invited me down to spend a little time with him," said Dean. "[Neil] said, 'Why don't you and I, once the boys go to bed, why don't we play a game of Risk.'"

I said I'd enjoy that. We started playing Risk and then he slipped me a piece of paper and said "read that." I did.

On that piece of paper there
was "That’s one small step for man, one giant leap for mankind." He
says, "What do you think about that?" I said "fabulous." He said, "I
thought you might like that, but I wanted you to read it.'"

He then added: "It was 'that is one small step for A man.'"

Armstrong always claimed he thought up the line after touching down
on the moon, but "he gave it a bit more thought than that," Dr.
Christopher Riley, the documentary's director, tells the Telegraph. "I
think the reason he always claimed he'd thought it up after landing was
that he was bombarded by suggestions in the run up to the mission, and
found them a distraction to the business of landing on the moon." In the
end, "it was probably easier to just say that he'd thought it up after
landing, thus dodging the issue of where the words came from." Well,
that makes sense, says Dina Spector at Business Insider.
Armstrong "was known for his modesty and camera-shy persona. He avoided
the press and relished his privacy, despite being hailed as a hero."